Matter degrees of freedom and string breaking in Abelian projected quenched SU(2) QCD

TL;DR

This paper numerically derives the effective Abelian action in quenched SU(2) QCD, demonstrating that Abelian matter fields are crucial for adjoint string breaking and that the phenomenon can be effectively described within the Abelian projection framework.

Contribution

It provides the first numerical derivation of the effective Abelian action including matter fields and shows their essential role in adjoint string breaking in quenched SU(2) QCD.

Findings

Abelian matter fields significantly contribute to the total action.

The adjoint string is observed to break using Abelian operators.

The adjoint string tension is mainly due to Abelian and monopole contributions.

Abstract

In the Abelian projection the Yang--Mills theory contains Abelian gauge fields (diagonal degrees of freedom) and the Abelian matter fields (off-diagonal degrees) described by a complicated action. The matter fields are essential for the breaking of the adjoint string. We obtain numerically the effective action of the Abelian gauge and the Abelian matter fields in quenched SU(2) QCD and show that the Abelian matter fields provide an essential contribution to the total action even in the infrared region. We also observe the breaking of an Abelian analog of the adjoint string using Abelian operators. We show that the adjoint string tension is dominated by the Abelian and the monopole contributions similarly to the case of the fundamental particles. We conclude that the adjoint string breaking can successfully be described in the Abelian projection formalism.